55 Engine idle-speed system modelling and control ... · Engine idle-speed system modelling and control optimization using artificial intelligence P K Wong1*, L M Tam1,KLi1, and C

Engine idle-speed system modelling and controloptimization using artificial intelligenceP K Wong1*, L M Tam1, K Li1, and C M Vong2

1Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Taipa, Macao2Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Taipa,

Macao

The manuscript was received on 6 March 2009 and was accepted after revision for publication on 30 June 2009.

DOI: 10.1243/09544070JAUTO1196

Abstract: This paper proposes a novel modelling and optimization approach for steady stateand transient performance tune-up of an engine at idle speed. In terms of modelling, Latinhypercube sampling and multiple-input and multiple-output (MIMO) least-squares supportvector machines (LS-SVMs) are proposed to build an engine idle-speed model based onexperimental sample data. Then, a genetic algorithm (GA) and particle swarm optimization(PSO) are applied to obtain an optimal electronic control unit setting automatically, undervarious user-defined constraints. All of the above techniques mentioned are artificial intelli-gence techniques. To illustrate the advantages of the MIMO LS-SVM, a traditional multilayerfeedforward neural network (MFN) is also applied to build the engine idle-speed model. Themodelling accuracies of the MIMO LS-SVM and MFN are also compared. This study shows thatthe predicted results using the estimated model from the LS-SVM are in good agreementwith the actual test results. Moreover, both the GA and PSO optimization results show animpressive improvement on idle-speed performance in a test engine. The optimization resultsalso indicate that PSO is more efficient than the GA in an idle-speed control optimizationproblem based on the LS-SVM model. As the proposed methodology is generic, it can beapplied to different engine modelling and control optimization problems.

Keywords: idle-speed control, least-squares support vector machines, control optimization,genetic algorithm, particle swarm optimization

1 INTRODUCTION

Nowadays, the automotive engine is controlled by

the electronic control unit (ECU), and the engine

performance at idle speed is significantly affected

by the set-up of control parameters in the ECU. In

modern spark ignition engines, an efficient idle-

speed performance is required to fulfil the ever-

increasing requirements on fuel consumption, vehi-

cle driveability, and pollutant emissions. Basically,

the idle-speed control problem is a compromise

among low engine speed for fuel saving, minimum

emissions, and disturbance rejection ability [1].

From the control point of view, the primary difficulty

with the idle-speed control (ISC) problem is that the

engine at idle is subject to step disturbances from

unknown external loads and accessory loads such as

air-conditioning or power steering loads, etc. These

disturbances decrease engine speed rapidly and

therefore must be rejected.

Currently, the engine idle-speed control para-

meters in the ECU for production cars are almost

formulated in control maps (look-up tables). There

are many maps around the target idle speed for the

engineer to set, such as fuel and ignition maps.

Current practice of engine idle performance tune-up

relies on the experience of the automotive engineer

who handles a huge number of combinations of

engine control parameters. Moreover, engine idle-

speed tune-up is done empirically through testes on

the dynamometer (dyno) [2]. As a result, a lot of time

*Corresponding author: Department of Electromechanical En-

gineering, Faculty of Science and Technology, University of

Macau, Taipa, Macao.

email: [email protected]

55

JAUTO1196 Proc. IMechE Vol. 224 Part D: J. Automobile Engineering

and resources are consumed, while the optimal

parameters may not be obtained.

Recently, researches have described the use of

some advanced idle-speed controllers, such as an

online proportional–integral–derivative (PID) tuning

controller [3], adaptive control algorithm [4], model-

based control algorithm [5], and robust control

algorithm [6, 7], to regulate the air control valve

(bypass air valve (BPAV) or electronic throttle) to

achieve a satisfactory idle-speed response. Never-

theless, the limitations and problems of these ad-

vanced controllers are as follows.

1. No matter how advanced the algorithms are, the

development of the control systems must call for

exact engine model and base system parameters

for system simulation and dynamic analysis. An

exact engine idle-speed model is also important

for model-based control algorithms. However, a

modern automotive engine model is a complex

multivariable non-linear function, which is very

difficult to be determined. Therefore the models

used in these sophisticated controllers are mostly

empirical models, which are derived from resort-

ing to some simple physics laws combined with

identification procedures for estimation of several

unknown parameters [8]. This kind of engine

model is quite simple as compared with the real

engine system [4] and only suitable for several

models of vehicle engines. In fact, many coeffi-

cients in the empirical models are also difficult

to determine. Therefore the empirical models

cannot reflect the actual performance of the

controller and cannot let the engineer truly

optimize the controller parameters.

2. The control variables and control objectives of

these intelligent controllers are incomprehensi-

ble. In the engine idle-speed system, ignition

timing, air control valve opening area or duty

cycle, and fuel injection time are significant

factors affecting the internally developed torque

and engine speed. However, since too many

assumptions are made to simplify the empirical

models, most of the sophisticated controllers

mentioned above only consider the air control

valve and/or ignition advance as direct control

parameters [3, 5–8]. Very little research considers

the fuel injection time, because all of these

advanced controllers assume that the base fuel

map is perfectly fine-tuned, and the fuel injection

time is adjusted according to the manifold air

pressure, which is indirectly controlled by the air

control valve. In fact, a base fuel map is quite

important to engine idle-speed stability, fuel

consumption, and emission quality, but it is very

difficult to get a perfect base map. Moreover,

most of the idle-speed control objectives in the

available literatures only focus on an idle-speed

response subject to external disturbances [3, 4, 6–

8]; there is no comprehensive discussion about

fuel consumption and emission quality together,

but these two factors are very important to the

ISC problem as well.

3. These intelligent controllers are still under inves-

tigation. Therefore, look-up tables together with

a typical PID controller are still popular today

when considering gasoline engine idle-speed

control [9].

In view of the above limitations of ISC map

calibration and advanced idle-speed controllers, de-

velopment of a comprehensive idle-speed system

modelling and control optimization method can con-

tribute to existing engine ISC system tune-up and

its controller development. The objective of this re-

search is not to design an advanced idle-speed con-

troller but to develop a comprehensive and reliable

engine modelling methodology, such that the devel-

opment of many intelligent idle-speed controllers can

couple with any tailor-made and practical engine

models built from this methodology for controller

design and simulation. In terms of ISC system tune-up

for current automobiles, by integrating proper com-

puter aided optimization methods with the engine

models built, an optimal ECU set-up can also be easily

determined. The car engine is only required to go

through a dyno test for verification after obtaining

a satisfactory set-up from the integrated approach.

Hence, the number of unnecessary dyno tests for the

trial set-up can be drastically reduced in order to save a

large amount of time and money for testing.

According to the above objectives, modelling of the

engine idle-speed system is an important part of this

research. To model a complicated system exactly,

whose domain information is insufficient, black-box

identification techniques are usually employed. These

techniques can quickly derive models from experi-

mental data [10]. The most common black-box mod-

elling technique for automotive engine modelling

uses neural networks. It is well known that a neural

network is a universal estimator. Recent researchers

have described the use of neural networks for mod-

elling some engine performances [11, 12] based on

experimental data. There are, in general, however, two

main drawbacks for neural networks [13].

1. The architecture, including the number of hidden

neurons, has to be determined a priori or

56 P K Wong, L M Tam, K Li, and C M Vong

Proc. IMechE Vol. 224 Part D: J. Automobile Engineering JAUTO1196

modified while training by heuristics, which res-

ults in a non-necessarily optimal network struc-

ture.

2. The training process (i.e. the minimization of the

residual squared error cost function) in neural

networks can easily become stuck by local mini-

ma. Various ways of preventing local minima,

like early stopping, weight decay, etc., are em-

ployed. However, those methods greatly affect

the generalization of the estimated function,

i.e. the capacity to handle new input cases.

With an emerging artificial intelligence technique

of least-squares support vector machines (LS-SVMs)

[14], combining the advantages of neural networks

(handling large amount of highly non-linear data)

and non-linear regression (high generalization), the

previous drawbacks from neural networks are over-

come. The main advantages of LS-SVM over neural

networks are good generalization, a guarantee of a

global solution having a minimal fitting error, and

the fact that the architecture of the model must not

be determined before training [15].

In view of the advantages of LS-SVMs, this paper

proposes to use this novel approach to model the

multivariable engine ISC system. The model then

serves as an objective function for optimization.

2 PROPOSED MODELLING AND OPTIMIZATIONFRAMEWORK

A schematic illustration of the framework and overall

methodology is shown in Fig. 1. The upper branch in

Fig. 1 shows the steps required to build the LS-SVM

model. The experiments are still required, but only

to provide sufficient data for LS-SVM training. The

design of experiments is used additionally to stream-

line the process of creating representative sampling

data points to train the model. Once the engine idle-

speed performance model obtained is evaluated, it is

then possible to use a computer aided technique

to search for the best engine control parameters

automatically based on the model, if the application

is required. As the model derived by an LS-SVM

is difficult to differentiate or is even non-differ-

entiable, gradient information of this model cannot

be easily obtained. Practically, direct search methods

are employed to determine the suboptimal solution

for this kind of model, because they do not require

any gradient information. A genetic algorithm (GA)

and particle swarm optimization (PSO) are two wide-

ly used direct search techniques, so both optimiza-

tion algorithms are proposed for this constrained

multivariable optimization problem. The optimal

set points by both optimizers are then sent back to

Fig. 1 Framework for optimization of engine idle-speed control parameters

Engine idle-speed system modelling and control optimization 57


the ECU to carry out evaluation tests and a com-

parison. The feasibility and efficiency of the two

optimization approaches can then be examined. All

of the techniques mentioned above are artificial

intelligence techniques.

The purpose of this paper is to demonstrate the

effectiveness of the proposed LS-SVM + GA/PSO

methods on engine ISC systems. It is important to

note that there are no apparent limits or constraints

in the number of input–output variables, idle-speed

controller types, and the formulation of the optimi-

zation objective function. Hence, the methodology is

generic, and its effectiveness is demonstrated in later

sections through a case study of the ISC optimi-

zation problem. It is believed that the proposed

methods can be applied to different engine model-

ling and control optimization problems.

3 IDLE-SPEED MODEL IDENTIFICATION

3.1 LS-SVM formulation for multivariablefunction estimation

The classical LS-SVM modelling algorithm is only a

multi-input but single-output modelling method.

However, the practical engine idle-speed system

modelling is a multi-input/multi-output (MIMO)

modelling problem. Hence, a new MIMO LS-SVM

modelling algorithm based on classical LS-SVM is

proposed in this paper. The concept is presented

below.

Consider a training dataset, D~f(xk,yk)gNk~1, with

N data points, where xk [Rn represents the kth engine

set-up and xk is an n-dimension system input vector,

and yk [Rm is the kth engine output based on xk, k 5 1

to N. Here, yk is an m-dimension system output

vector, yk 5 [yk,1,…,yk,m]. For example, yk,1 could be

the minimum idle speed and yk,m could be the fuel

consumption. For the automotive engine, each out-

put performance in the dataset yk is usually an

individual variable and able to be measured sepa-

rately, so the training dataset D can be arranged as

D~ d1, . . . ,dh, . . . ,dmf g ð1Þ

where dh~f(xk,yk,h)gNk~1; h [ [1,m]. In this case, for

each single output dimension in yk, it forms a new

training dataset dh. Consequently, the MIMO train-

ing dataset D is separated into m multi-input but

single-output subtraining datasets dh. For each

multi-input single-output dataset dh, LS-SVM deals

with the following optimization problem in the

primal weight space

minwh,bh,eh

JP(w,eh)~ 12 wT

hwhzch12

Pnk~1

e2k,h

such that ek,h~yk,h{½wThw(xk)zbh�, k~1, . . . ,N

264

375ð2Þ

where ch [R is a scalar for the regularization factor

(which is a hyper-parameter for tuning), wh[Rnh is

the weight vector of the target function, eh 5 [e1,h,…,

eN,h] is the residual vector, and w : Rn?Rnh is a non-

linear mapping. The estimated model Mh(x) is con-

sidered as

Mh(x)~wThw(x)zbh ð3Þ

However, wh may be in very high or even infinite

dimensions that cannot be solved directly. In order

to resolve the problem, the Lagrangian of equation

(2) is constructed to derive the dual problem and the

Lagrangian is as follows

Lh(wh,bh,eh,ah)

~Jp(wh,eh){Xn

k~1

ak,hfwTh w(xk)zbhzek,h{yk,hg

ð4Þ

where ak,h [ ah are Lagrange multipliers. The condi-

tions for optimality are given by

LLh

Lwh~0?wh~

Xn

k~1

ak,hw(xk)

LLh

Lbh~0?

Xn

k~1

ak,h~0

LLh

Leh~0?ak,h~chek,h

LLh

Lah~0?wT

hw(xk)zbhzek,h{yk,h~0, k~1,:::,N

ð5Þ

After elimination of the variables wh and eh in

equation (4) using the results from equation (5), the

LS-SVM dual formulation of the non-linear function

estimation is then expressed as follows [14]

Solve in ah, bh :

0 1Tv

1v Vz 1ch

IN

" #bh

ah

� �~

0

yh

� �264

375 ð6Þ

where yh 5 [y1,h,…, yN,h]T and ah 5 [a1,h,…, aN,h]T. The

kernel trick is employed as follows



Vk,l~w(xk)Tw(xl)

~K (xk,xl), k,l~1, . . . ,N ð7Þ

The resulting LS-SVM model for the function esti-

mation is constructed by substituting the results of

equation (5), i.e. wh~XN

k~1ak,hw(xk), into equation

(3) and becomes

Mh(x)~XN

k~1

ak,hw(xk)Tw(x)zbh

~XN

k~1

ak,hK (xk,x)zbh

~XN

k~1

ak,h exp {xk{xk k2

s2h

!zbh ð8Þ

where ak,h, bh [R are the solutions of equation (6), xk

is the kth engine set-up in the training dataset dh, x

is the new input set-up for the engine idle perfor-

mance prediction, and the radial basis function is

chosen as the kernel function K, which is the

common choice for modelling. In the radial basis

function, sh specifies the kernel sample variance,

which is also a hyperparameter for tuning, and I?Imeans Euclidean distance. After inferring m pairs of

hyperparameters (ch, sh) by a well-known technique,

Bayesian inference [14], m individual training data-

sets are used for calculating m individual sets of

support vectors ak,h and threshold values bh. Finally,

m individual sets of Mh(x) can be constructed based

on equation (8). The whole MIMO modelling algo-

rithm is shown in Fig. 2.

In Fig. 2, a set of LS-SVM models are generated to

predict the engine response under different combi-

nations of control variables. Each model represents

one engine output performance, which is included

in the objective function for optimization.

3.2 Experimental set-up and data sampling forthe case study

To demonstrate the effectiveness of the whole

modelling and optimization approach, an optimiza-

tion of the engine idle-speed controller together with

the ECU set-up was selected as a case study. The test

car used in the case study was a Honda Integra DC5

Type-R with a K20A DOHC i-VTEC engine. The

manifold absolute pressure (MAP) of the test engine

at idle was controlled by a BPAV. Although the use of

an electronic throttle becomes more and more

prevalent, the method is equally applicable to both

the electronic throttle and BPAV.

Taking the demonstration purpose into account,

an aftermarket programmable ECU, MoTeC M800,

was selected as the calibration and optimization test

bed. The fuel injection time, valve timing and

ignition control signals were stored in its look-up

tables. Moreover, a PID controller using the engine

idle speed as the feedback signal was applied to the

BPAV due to its popularity among modern spark

ignition automobiles. The control scheme of MoTeC

M800 is shown in Table 1.

Fig. 2 MIMO LS-SVM modelling framework



To check the robustness of the control settings, the

test car was loaded on a chassis dyno (Fig. 3) and a

constant step load provided by the dyno was applied

to the engine. Then the engine speed and lambda (l)

variations were measured. The engine idle perfor-

mance data were also recorded by the ECU at a

logging rate of 20 Hz. Figure 4 shows the constant

step load applied by the dyno in the course of data

sampling. The magnitude of the constant load was

measured from the total accessory loads of the test

car including the electrical, air-conditioning, and

power-steering loads. Because of a high-speed cam

used in the test engine, the aimed engine idle speed

was set to be 1200 r/min in the case study. It is well

known that setting a stable idle speed for a high-

speed cam is a challenging job.

In this case study, the following engine idle-speed

system parameters were selected to be the input and

output variables of the MIMO LS-SVM model

x~vF i,j, I i,j, V j, Pro, Int, Der, Nor, Lw

y~vIAER, IAEl,X

F , Rmin, Trisew

ð9Þ

There are two types of variables in equation (9):input variables and output variables. It was assumedthat the input variables are

Fi, j 5 fuel injection time at the corresponding MAP

i and idle speed j (ms, i 5 [20, 30, 40, 50],

j 5 [500, 1000, 1500])

Ii, j 5 ignition advance at the corresponding MAP i

and idle speed j (degree before top dead

centre (BTDC), i 5 [20, 30, 40, 50], j 5 [500,

1000, 1500])

Table 1 Control scheme of MoTeC M800

Control variable Type of control scheme

Fuel injection time Open loop 3-D look-up tableValve timing Open loop 2-D look-up tableIgnition advance Open loop 3-D look-up tableMAP PID BPAV controller

Fig. 3 Experimental set-up for data sampling and programmable ECU

Fig. 4 Constant step load applied by the chassis dyno in the case study



Vj 5 intake valve open timing at the corresponding

idle speed j (degree BTDC, j 5 [500, 1000, 1500])

Pro 5 proportional gain of the idle air valve

controller

Int 5 integral gain of the idle air valve controller

Der 5 derivative gain of the idle air valve controller

Nor 5 normal position of the idle air valve (per-

centage of wide open)

L 5 constant step load applied to the engine

(percentage of the dyno full load)

It was also assumed that the output variables are:

IAER 5 integral absolute error of the engine idle

speed (r/min), which is calculated by

IAER~Xtf

t~0

Rt{Raimj j ð10Þ

where, for this case study, tf 5 15 s and Raim 5

1200 r/min.

IAEl 5 integral absolute error of lambda

IAEl~Xtf

t~0

lt{laimj j ð11Þ

where, for this case study, laim 5 1.

SF 5 overall fuel consumption (ms), where the

fuel consumption is proportional to the fuel

injection time, and hence the overall fuel

consumption can be estimated by the sum-

mation of fuel injection from t 5 0 to tf 5 15 s

with sampling time 5 0.05 s

Rmin 5 minimum idle speed to which the engine

falls when a step load is applied (r/min)

Trise 5 recovery time to aimed speed when a step

load is applied (s)

A design of experiment technique, Latin hyper-

cube sampling (LHS) [16], was employed to choose

a representative set of operating points for genera-

ting training samples. A total of 200 sets of repres-

entative combinations of input variables were select-

ed and downloaded to the ECU to produce 200 sets

of output performance data. Figures 5 to 7 show an

example of output performance of Dbest, which is

the best performance among the 200 sample datasets.

The ECU set points of Dbest are shown in Table 2.

In order to have a fair comparison with the engine

idle performances under different input set-ups, all

the engine training data were recorded 5 seconds

before the load was applied and 10 seconds after

that point. Figure 5 shows the idle-speed regulation

performance of Dbest. When the load is applied, the

engine speed first falls to 602 r/min and then takes

1.05 s to recover. The integral absolute error, which

represents the idle-speed regulation ability, in the

15 s test period is 6192.36 r/min. Meanwhile, the

engine lambda value, as shown in Fig. 6, rises first,

which is due to the fact that if the engine speed

suddenly drops, the fuel injection time also drops

accordingly (Fig. 7). When the BPAV controller starts

to take action, it tends to open widely to increase the

MAP, resulting in an increase in the amount of fuel

injected into the intake manifold. In this way, more

Fig. 5. Idle-speed regulation performance in Dbest



Fig. 6 Lambda performance in Dbest

Fig. 7 Fuel consumption in Dbest

Table 2 ECU set points of Dbest

Engine speed(r/min)

Fi, j Ii, j

Vj

MAP (kPa) MAP (kPa)

20 30 40 50 20 30 40 50

500 3.04 3.24 3.36 4.02 7.9 8.6 9.4 10 21000 2.89 3.27 3.39 4.06 14.5 15 15.7 16 61500 3.04 3.31 3.36 4.09 15.9 16.8 17.3 18 8

BPAV controller parameters Pro Int Der Nor2.24 0.87 1.32 40.24



air–fuel mixture can be breathed into the combus-

tion chamber to generate more torque in order to

counteract the load and regain the aimed speed. This

is noted that there is a time delay between the fuel

injection and the lambda value. This is because the

lambda value is measured by an oxygen sensor in the

exhaust pipe and the value can only represent the

stoichiometric ratio in the previous combustion

cycle.

3.3 Application of the MIMO LS-SVM andmodelling results

In the current application, Mh(x), h 5 1, 2,…, 5, in

equation (8) stands for the performance functions of

IAER, IAEl, SF, Rmin, Trise respectively. After collec-

tion of the sample dataset D, for every data subset

dh [D, it was randomly divided into two sets: TRAINh

for training and TESTh for testing, where TRAINh

contains 80 per cent of dh and TESTh holds the

remaining 20 per cent. Then TRAINh was sent to the

LS-SVM module for training, which had been

implemented using LS-SVMlab 1.5 [17], a Matlab

toolbox under MS Windows XP.

In order to have a more accurate modelling result,

the input data of the training dataset is convention-

ally normalized before training [18]. This prevents

any input parameter from dominating the output

value. For all input values, it is necessary to be

normalized within the range [0, 1], i.e. unit variance,

through the following equation

v�~v{vmin

vmax{vminð12Þ

For example, v [ [2, 35], vmin 5 2, and vmax 5 35. The

limits for each input control parameter are deter-

mined via a number of experiments, expert knowl-

edge, and manufacturer data sheets. After obtaining

the optimal setting, each set point should go through

a denormalization using the inverse of equation (12)

in order to obtain the actual value v. The process

flow of the normalization and denormalization is

shown in Fig. 1.

To verify the accuracy of each function of Mh(x),

an error function is proposed. For a certain function

Mh(x), the corresponding validation error is

Eh~

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

XN

k~1

yk,h{Mh(xk)

yk,h

� �2

vuut ð13Þ

where xk is the engine control parameters of the kth

data point in TESTh, yk,h is the actual performance

output value in the data point dk (dk(xk, yk,h)

represents the kth data point in dh), and N is the

number of data points in the test set. The error Eh is

a root-mean-square of the difference between the

true value yk,h and its corresponding estimated value

from Mh(xk). The difference is also divided by yk,h, so

that the result is normalized within the range [0, 1].

Hence, the accuracy rate for each output function

Mh(x) is calculated using the following formula

Accuracyh~(1{Eh)|100 % ð14Þ

All the output functions were evaluated one by one

against their own test sets TESTh using equation

(14). Table 3 shows that the predicted results are in

good agreement with the actual experiment results

under their hyperparameters (ch, sh) inferred using

Bayesian inference. Hence, the idle-speed system

model that was built is reliable and can be used for

optimization. However, it is believed that the model

accuracy could be improved by increasing the num-

ber of training data.

3.4 Application of neural network and modellingresults

To illustrate the advantages of MIMO LS-SVM re-

gression, the modelling results were compared with

those obtained from training a multilayer feed for-

ward neural network (MFN) with back-propagation.

Since the MFN is similar to the MIMO LS-SVM and

is also a well-known universal estimator, the results

from the MFN can be considered as a rather stan-

dard benchmark.

Table 3 Accuracy of different output functions Mh(x) and its corresponding hyperparameters

Engine output function Mh(x) ch sh Training error with TRAINh (%) Average accuracy with TESTh (%)

M1(x) 2796.40 70.04 1.75 95.72M2(x) 190.53 53.54 2.43 96.14M3(x) 1546.34 1264.26 6.45 94.52M4(x) 2426.72 61.86 1.34 95.41M5(x) 3349.90 44.69 3.65 93.52

Overall average 3.12 95.06



A neural network with five output neurons

NETh 5 {NET1, NET2, NET3, NET4, NET5}, which res-

pectively represent the performance functions of

IAER, IAEl, SF, Rmin, Trise, was built based on the

same training dataset. The neural network consists

of 32 input neurons (i.e. the input parameters x), 5

output neurons, and 50 hidden neurons. Normally,

50 hidden neurons can provide enough capability

to approximate a highly non-linear function. The

activation function used inside the hidden neurons

was the Tan-Sigmoid transfer function, while for the

output neurons, a pure linear filter was employed

(Fig. 8).

The training method employed the standard back-

propagation algorithm (i.e. a gradient descent to-

wards the negative direction of the gradient), so

that the results of the MFN can be considered as a

standard. The learning rate of the weight update was

set to be 0.05. The same test sets were also chosen so

that the accuracies of the engine idle-speed perfor-

mance functions built by the MIMO LS-SVM and

MFN can be compared reasonably. The training

results of the neural network are shown in Table

4. The average accuracy of each output shown in

Table 4 is calculated by using equation (14).

3.5 Comparison of modelling results

With reference to Tables 3 and 4, the MIMO LS-SVM

outperforms the MFN by about 11.40 per cent in

overall average accuracy under the same test sets. In

the MIMO LS-SVM, two sets of hyperparameters (ch,

sh) are required. These hyperparameters can be

inferred automatically by using Bayesian inference,

which totally eliminates the user burden. In the

MFN, the learning rate and number of hidden

neurons are required from the users. Surely, these

parameters can also be solved by 10-fold cross-

validation. However, the users have to prepare a grid

of guessed values for these parameters, and the grid

may not cover the best values for the parameters.

Therefore, the MIMO LS-SVM could often produce a

better generalization rate over the MFN, as indicated

in Tables 3 and 4. The MFN produces less training

errors than the MIMO LS-SVM because there is no

regularization factor controlling the tradeoff be-

tween training error and generalization. In contrast,

the MIMO LS-SVM produces better generalization

due to the regularization factor ch introduced in

the training error function.

4 IDLE-SPEED CONTROL OPTIMIZATION

After obtaining the idle-speed model, it is then

possible to use the GA and PSO to search the best

engine ISC set-up automatically. In this application,

the engine set-up involves 31 variables, so it is a large-

scale and challenging optimization problem. Nowa-

days, the GA has become a well-known technique for

Fig. 8 Architecture of the MFN

Table 4 Accuracy of different output functions NETh

Engine output function Mh(x) Training error with TRAINh (%) Average accuracy with TESTh (%)

M1(x) 5 NET1(x) 0.16 86.43M2(x) 5 NET2(x) 0.24 84.35M3(x) 5 NET3(x) 0.65 80.37M4(x) 5 NET4(x) 0.82 81.72M5(x) 5 NET5(x) 0.03 85.44

Overall average 0.38 83.66



solving many engineering optimization problems.

Moreover, it has been proved effective in solving

both constrained and un-constrained objective func-

tions with discontinuous, non-differentiable, sto-

chastic, and highly non-linear, etc., properties [19,

20]. On the other hand, PSO is a relatively new

algorithm proposed by Kennedy and Eberhart in

1995 [21]. As a form of swarm intelligence, PSO is a

population-based stochastic optimization technique

inspired by the social behaviour of bird flocking or

fish schooling. Basically, PSO is also an evolutionary

computation technique similar to the GA. However,

it has no evolutionary operators of crossover and

mutation as compared with the GA. From the user

point of view, PSO can reduce the time and the

burden for users trying different evolutionary opera-

tors to find the optimal solution.

Since both the GA and PSO have their own pros

and cons, these two optimization methods are

studied in this paper. However, direct search meth-

ods can easily suffer from a local optimum. In

order to minimize the chance of obtaining a local

optimum, different and arbitrarily generated initial

populations are used. To achieve such a purpose, 10

sets of independent optimization runs were carried

out for each method. The optimization results of

both optimization algorithms are also compared at

the end of this section.

4.1 Objective function for engine ISCoptimization

An objective function was designed to evaluate the

idle performance under different control set-ups. In

the case of engine ISC optimization, a complete

evaluation function should encompass the following

[22].

1. Idle-speed regulation. The engine idle speed must

be capable of maintaining close to the target

point with deviation as low as possible. Essen-

tially, the better the idle-speed regulation and

disturbance rejection ability, the lower the aimed

idle speed can be set.

2. Robustness of load disturbance. In a vehicle, the

disturbance is due to electrical loads (e.g. switch-

ing on or off the air-conditioning, window

heating, light, etc.), power steering, and low-

speed manoeuvring. These are events that, when

they occur, may cause the engine to stall.

3. Fuel economy and emissions. On average, vehi-

cles consume about 30 per cent of their fuel in

idling during city driving [23], so minimization of

fuel consumption and pollutant emissions at idle

speed is very important.

Hence a well-considered objective function, fobj, is

formulated in the following equation, where it is

shown that the larger the fitness value calculated by

the objective function, the better the engine idle-

speed performance

fobj~Max½Fitness�

~Max½{wIAERtan{1(M1(x))

{wIAEltan{1(M2(x)){wPF tan{1(M3(x))

zwRmintan{1(M4(x)){wTrise

tan{1(M5(x))�ð15Þ

Subject to

2!F i,j!5 ms

0!I i,j!300 BTDC

{30!V j!300 BTDC

L~20%

where M1(x) represents the idle-speed regulation

quality, M2(x) represents the idle-speed emission

quality (ideally when the stoichiometric ratio l 5 1,

the catalytic converter gains the maximum conver-

sion efficiency of the exhaust gas), M3(x) is employed

to assess the idle-speed fuel consumption, and M4(x)

and M5(x) are used together for assessing the idle-

speed load rejection ability. In this case study, wIAER,

wIAEl, wPF , wRmin

, and wTrisewere set to be 3, 2, 3, 4,

and 1 respectively. Each performance index is also

transformed to a scale of (0, p/2) by tan21(?) in

equation (15). This ensures that each index has the

same contribution to the objective function. The

objective function is manipulated by the two opti-

mizers for generating the best ISC settings.

4.2 GA optimization results

The GA optimization framework was implemented

using Matlab. By testing various crossover and muta-

tion methods for this application, the GA operators

and parameters as shown in Table 5 were selected

to ensure maximum efficiency and accuracy.

Table 6 shows 10 sets of optimization results

obtained by the GA. The 10 sets of optimization

results differ from each other. This is because the GA

is initialized with random start points within the

search space and the search result is very sensitive to



the initial values. The best fitness value out of 10 is

26.7010 and its optimal set points are shown in

Table 7.

4.3 PSO results

The PSO framework was also implemented using

Matlab. In PSO, the population is called a swarm and

the individuals (i.e. different combinations of ECU

set points x) are called particles. Regarding an n-

dimensional search space and a swarm consisting of

M particles, the ith particle is represented by an n-

dimensional vector xi 5 (xi1, xi2, …, xin), the velocity

of this particle is an n-dimensional vector vi 5 (vi1,

vi2, …, vin), and the best previous position encoun-

tered by this particle is described by pi 5 (pi1, pi2, …,

pin). Let g represent the index of the particle that

attains the best previous position among all the

particles in the swarm. Then, the swarm is manipu-

lated in accordance with the following equations [24,

25]

vi(jz1)~wcvi(j)zc1r1½pi(j){xi(j)�zc2r2½pg (j){xi(j)�

ð16Þ

xi(jz1)~xi(j)zvi(jz1) ð17Þ

where i is the particle index i 5 [1, 2, …, M]. The

selection of the above parameters was widely studied

in the relevant literature [24, 26]. With reference to

the literature, the PSO parameters as shown in

Table 8 were selected for this case study.

Table 9 shows 10 sets of optimization results ob-

tained by PSO. Although it is also initialized arbi-

trarily, the standard deviation of PSO in Table 9 is

only 0.0229, which is much less than 0.0583 of the

GA shown in Table 6. In other words, the PSO results

are more stable than those of the GA. This is because

PSO is somehow insensitive to the initial values. The

best fitness value of PSO in Table 9 is 26.6666 and

its optimal set points are shown in Table 10. It is also

found that the best fitness value of PSO (26.6666) is

larger than that of the GA (26.7010).

Table 6 Optimization results of 10 independent runs of GA

Result set IAER (r/min) IAEl SF (ms) Rmin (r/min) Trise (s) Fitness

1 5665.17 5.97 273.92 741 1.52 26.91742 6135.25 5.46 293.51 778 1.53 26.88863 5787.51 4.94 277.23 846 1.57 26.84544 5013.49 5.14 351.31 672 1.15 26.70105 5822.16 4.65 276.14 934 1.44 26.79496 5390.34 4.79 276.12 883 1.45 26.80667 5882.28 4.89 271.56 931 1.42 26.82548 6147.47 4.73 246.02 998 1.53 26.84169 6193.63 4.38 252.31 1063 1.55 26.804810 6467.42 4.57 259.57 1093 1.61 26.8440

Standard deviation 0.0583

Table 5 GA operators and parameters

Number of generation 1000Population size 50Selection method Standard proportional selectionCrossover method Simple crossover with

probability 5 80%Mutation method Hybrid static Gaussian and

uniform mutation withprobability 5 40% and standarddeviation 5 0.2

Table 7 Optimal set points recommended by GA

Engine speed (r/min)

Fi, j Ii, j

Vj

MAP (kPa) MAP (kPa)

20 30 40 50 20 30 40 50

500 1.99 2.11 2.23 3.39 11.1 11.9 12.6 13.2 0.41000 1.91 2.13 2.25 3.34 13 14 15.4 14.9 8.11500 2.12 2.25 2.25 3.55 16.6 16.9 17.8 18.5 10.3


Table 8 PSO parameters

Number of generation 1000Population size 50wc 0.9c1 2c2 2



4.4 Evaluation of optimization results

To check the feasibility and efficiency of the metho-

dology, the optimal settings found by the GA and

PSO were then sent back to the ECU and evaluation

tests were carried out using the chassis dyno. Fig-

ures 9 to 11 present the actual engine idle perfor-

mance based on the optimal settings.

Figure 9 shows the idle-speed regulation perfor-

mance using the optimal settings found by both

optimizers. Before the load is applied, both engine

idle speeds run steady and closely to the aimed

speed. When the load is applied, the engine using

the set points recommended by the GA falls to a

minimum speed of 641 r/min and then takes 1.18 s

to recover. On the contrary, the engine using the set

points recommended by PSO falls to a minimum

speed of 723 r/min and then takes 1.1 s to recover. As

compared with the steady state idle-speed perfor-

mance of Dbest in Fig. 5, the speed fluctuation at

Table 9 Optimization results of 10 independent runs of PSO

Result set IAER (r/min) IAEl SF (ms) Rmin (r/min) Trise (s) Fitness

1 4807.36 5.02 357.82 695 1.04 26.69282 4996.41 4.82 356.83 724 1.02 26.66663 5228.35 5.03 361.54 747 1.00 26.67074 5095.62 5.02 362.66 740 1.00 26.67255 4860.74 4.81 357.01 727 1.01 26.66056 4908.31 4.90 369.43 717 0.97 26.64537 4812.84 5.05 359.84 689 0.94 26.64288 4736.69 4.87 345.53 665 0.92 26.61899 4804.78 5.11 355.62 639 0.95 26.654010 4915.12 5.14 337.77 609 1.03 26.6935

Standard deviation 0.0229

Table 10 Optimal set points recommended by PSO

Engine speed(r/min)

Fi, j Ii, j

Vj

MAP (kPa) MAP (kPa)

20 30 40 50 20 30 40 50

500 1.96 2.05 2.17 3.28 10.8 11.7 12.6 13.2 0.01000 1.9 2.13 2.27 3.31 11.9 13.4 15.7 16.4 4.31500 2.12 2.18 2.23 3.47 14.7 15.2 16.7 17.3 6.7


Fig. 9 Actual idle-speed regulation performance using the optimal settings of the GA and PSO



steady state can be improved using both optimal

settings. Figure 10 shows the engine lambda per-

formance using the optimal settings of the two

optimizers. As compared with the lambda perfor-

mance of the GA, the performance of PSO is closer to

the target lambda value along the test. Figure 11

shows that the overall fuel consumption of PSO is

also lower than that of the GA. Table 11 shows a

comparison among the optimization results, actual

test results, and the results of Dbest. The accuracies

in Table 11 show that both the GA and PSO results

are in good agreement with the actual test results.

These verify again that the engine idle-speed model

built by the MIMO LS-SVM is accurate and reliable.

In Table 11, the actual test results using the set

points produced by the GA outperform Dbest by

Fig. 10 Actual lambda performance using the optimal settings of the GA and PSO

Fig. 11 Actual fuel consumption using the optimal settings of the GA and PSO



about 17.20, 19.35, 17.97, and 6.48 per cent in the

actual idle-speed regulation ability, emission quality,

fuel consumption, and minimum idle speed respec-

tively, whereas the actual test results using the set

points produced by PSO outperform Dbest by about

27.89, 23.81, 23.38, and 20.04 per cent in the same

four performance indexes respectively. These verify

that both optimization algorithms are effective. The

recovery time of the idle speed is sacrificed in the

objective function, wTrisewas set to be the lowest

value in this case study, so the recovery time based

on the GA and PSO optimal settings is 12.38 and 4.00

per cent longer than that of Dbest respectively.

However, the recovery time is still acceptable.

Table 11 also indicates that the actual engine idle-

speed regulation ability, emission quality, fuel con-

sumption, minimum idle speed, and recovery time

of PSO are respectively 12.91, 5.54, 6.60, 12.74, and

6.78 per cent better than the corresponding values of

the GA. The above results show that PSO is superior

to the GA in this case study. The reason may be that

the mechanism of PSO can generate more diverse

populations during the whole iteration process.

5 CONCLUSIONS

This paper proposes a novel methodology for engine

idle-speed system modelling and optimization. The

approach uses a novel MIMO LS-SVM + LHS frame-

work for modelling and a multi-objective GA/PSO

framework to manipulate the engine model built to

determine the best combination of control para-

meters automatically. A case study successfully

demonstrates its application to a real automotive

engine. Evaluation tests show that the predicted

results using the estimated model from the MIMO

LS-SVM are in good agreement with the actual test

results. In comparison with the ordinary neural

network modelling approach, the novel MIMO LS-

SVM outperforms by about 11.40 per cent in overall

accuracy under the same test dataset. The optimiza-

tion results in Tables 6, 9, and 11 show that PSO is

superior to the GA under the LS-SVM model. An

impressive improvement in engine idle performance

is also achieved using the optimal setting generated

by PSO. Both prediction and experimental results

indicate that the proposed methodology (LHS +MIMO LS-SVM + PSO) can really produce reliable

and high-quality engine idle-speed performance.

In addition, this research is also a first attempt

at integrating a couple of paradigms (LHS, MIMO

LS-SVM and GA/PSO) into a general framework for

constrained multivariable optimization problems

under insufficient system information. The idle-

speed problem presented in this paper is to optimize

a lot of ECU base map variables and air valve con-

troller parameters for maximizing engine idle-speed

regulation quality, load rejection ability, emission

quality, and fuel economy all together. Therefore the

variables and optimization objectives involved in

this paper are more comprehensive and practical

than the schemes presented in the existing literature.

From the perspective of automotive engineering,

the integrated modelling and optimization metho-

dology is a new approach and can be applied to the

following engine set-up and control problems.

1. Engine tune-up and ECU calibration. Compared

to the conventional manual tuning approach for

current production car engines, the proposed new

methodology can greatly reduce the number of

expensive dyno tests. This saves not only the time

taken for optimal tune-up but also a large amount

of resources. It is also believed that the optimi-

zation results can be further improved if more

training data are added to the LS-SVM model.

2. Engine idle-speed system identification and con-

troller design. The proposed modelling approach

can be employed to build many types of practical

Table 11 Comparison between optimization results and actual test results and Dbest

IAER (r/min) IAEl SF (ms) Rmin (r/min) Trise (s) Fitness

Dbest 6192.36 6.72 462.01 602 1.05 26.7972GA optimization results (GAO) 5013.49 5.14 351.31 672 1.15 26.7010PSO optimization results (PSOO) 4996.41 4.82 356.83 724 1.02 26.6666GA actual test results (GAA) 5127.36 5.42 379.34 641 1.18 26.7490PSO actual test results (PSOA) 4465.42 5.12 354.06 723 1.10 26.7036Accuracy of GA results (GAO relative to

GAA)97.78% 94.83% 92.61% 95.16% 86.36% 99.29%

Accuracy of PSO results (PSOO relative toPSOA)

88.11% 94.14% 99.20% 99.76% 90.48% 99.45%

Actual improvement of GA (GAA relative toDbest)

17.20% 19.35% 17.97% 6.48% 212.38% 0.71%

Actual improvement of PSO (PSOA relativeto Dbest)

27.89% 23.81% 23.38% 20.04% 24.00% 1.38%

Comparison between PSOA and GAA (PSOA

relative to GAA)12.91% 5.54% 6.60% 12.74% 6.78% 0.84%



engine models exactly, and those models can be

employed to reflect the true engine performance

for advanced idle-speed controller design. In

comparison with the traditional engine models

used in the advanced controllers, such as neural

networks and empirical models, the proposed

modelling approach produces better generali-

zation and accuracy. Moreover, the proposed

modelling and/or optimization alogrithms can

be used as core components by some advanced

model reference controllers, such as model ref-

erence adaptive controllers, model identification

adaptive controllers, and model-based predictive

controllers, etc.

ACKNOWLEDGEMENTS

The research is supported by the University ofMacau Research Grant UL011/09-Y1/EME/WPK01/FST and the Science and Technology DevelopmentFund of Macau, Grant 019/2007/A.

F Authors 2010

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APPENDIX

Notation

bh bias of the hth engine model

c1 cognitive parameter

c2 social parameter

dh subtraining dataset for each single

output dimension yh

dk kth data point in dh

D training dataset

Dbest best performance set-up among the

200 sample datasets

Der derivative gain of the idle air valve

controller

eh residual vector for the hth engine

model

Eh root-mean-square error of the hth

engine model

Fi,j fuel injection time at the corre-

sponding MAP i and idle speed j

h engine performance model index

i particle index of PSO

IAER integral absolute error of engine idle

speed

IAEl integral absolute error of lambda

Ii,j ignition advance at the correspond-

ing MAP i and idle speed j

Int integral gain of the idle air valve

controller

IN N-dimensional identity matrix

j iteration counter of PSO

K predefined kernel function

L constant step load

m dimension of yk

Mh(x) hth engine performance model

n dimension of xk

nh dimension of the unknown feature

space

N number of data points in D

Nor normal position of the idle air valve

NETh(x) hth engine performance model

trained by the neural network

pg best previous position among all

particles

pi best previous position encountered

by the ith particle

Pro proportional gain of the idle air valve

controller

r1, r2 random numbers uniformly

distributed between 0 and 1

Raim aimed idle speed

Rmin minimum idle speed under a step

load

Rt engine idle speed at the correspond-

ing time t

tf data recording time

TESTh test dataset for the hth engine

model

TRAINh training dataset for the hth engine

model

Trise recovery time to aimed speed under

a step load

v input control parameter before

normalization

v* normalized input control parameter

vmax upper limit of the input control

parameter before normalization

vmin lower limit of the input control

parameter before normalization

vi velocity of the ith particle in PSO

Vj intake valve open timing at the

corresponding idle speed j

wc inertial weight

wh weight vector of the hth engine

model

wIAERuser-defined weight of engineidle-speed regulation

wIAEluser-defined weight of engineidle-speed emission quality

wRminuser-defined weight of minimum idlespeed

wTriseuser-defined weight of recovery timeto aimed speed

wSF user-defined weight of engineidle-speed fuel economy

x input engine set-up of the engine

performance model

xi ith particle vector in PSO

xk kth engine set-up in the training

dataset D

y output vector of the engine perfor-

mance model

yh hth engine output performance data

in y

yk kth engine output performance

training data based on the kth engine

set-up xk



yk,h hth engine output performance data

point in yk

ah support vector of the hth engine

model

ch regularization scalar factor of the hth

engine model

laim target lambda value

lt engine lambda value at the corre-

sponding time t

sh kernel sample variance of the hth

engine model

SF overall fuel consumption

1v N-dimensional vector 5 [1 … 1]T



55 Engine idle-speed system modelling and control ... · Engine idle-speed system modelling and control optimization using artificial intelligence P K Wong1*, L M Tam1,KLi1, and C

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